Classifying Stars - The Hertzsprung -Russell Diagram Classifying Stars - the Hertzsprung-Russell Diagram There are a few hundred billion stars in our galaxy, the Milky Way and billions of galaxies in the Universe. One important technique in science is to try and sort or classify things into groups and seek out trends or patterns. Astronomers do this with stars. So far we have discussed the luminosity and colour or effective temperature of stars. These can be plotted to form what is one of the most useful plots for stellar astronomy, the Hertzsprung-Russell (or H-R) diagram. It is named after the Danish and American astronomers who independently developed versions of the diagram in the early Twentieth Century. In an H-R diagram the luminosity or energy output of a star is plotted on the vertical axis. This can be expressed as a ratio of the star's luminosity to that of the Sun; L*/Lsun. Astronomers also use the historical concept of magnitude as a measure of a star's luminosity. Absolute magnitude is simply a measure of how bright a star would appear if 10 parsecs distant and thus allows stars to be simply compared.

Just to confuse things, the lower or more negative the magnitude, the brighter the star. By definition a star of magnitude 1 is 100 × brighter than one of magnitude 6. Our Sun has an absolute magnitude of + 4.8. Credit: CSIRO Possible axes for a Hertzsprung-Russell Diagram. Note how the temperature scale is reversed on the horizontal axis. Also take care if using magnitude to work upwards to negative values. The effective temperature of a star is plotted on the horizontal axis of an H-R diagram . One quirk here is that the temperature is plotted in reverse order, with high temperature (around 30,000 - 40,000 K) on the left and the cooler temperature (around 2,500 K) on the right. In practice astronomers actually measure a quantity called colour index that is simply the difference in the magnitude of a star when measured through two different coloured filters. Stars with a negative colour index are bluish whilst cooler orange or red stars have a positive colour index. The third possible scale for the horizontal axis is a star's spectral class. By splitting the light from a star through a spectrograph its spectrum can be recorded and analysed.

Stars of similar size, temperature, composition and other properties have similar spectra and are classified into the same spectral class. The main spectral classes for stars range from O (the hottest) through B, A, F, G, K and M (coolest). Our Sun is a G-class star. By comparing the spectra of an unknown star with spectra of selected standard reference stars a wealth of information, including its colour or effective temperature can be determined. If we now plot a Hertzsprung-Russell diagram for a few thousand nearest or brightest stars we see the following: Each dot represents a star. As we can see, stars do not appear randomly on the plot but appear to be grouped in four main regions. This is highly significant as it suggests that there may be some relationship between the luminosity and temperature of a star. Whilst not surprising (indeed we have already seen that a hotter star emits more energy per unit surface area than a cooler star) the relationship is complicated by the presence of these four groups. Let us examine these more closely. Most stars seem to fall into group A.

It shows a general trend from cool, dim stars in the lower right corner up to hot, extremely bright stars in the top left corner which fits in with our expected relationship between temperature and luminosity. This group is called the Main Sequence so stars found on it are main sequence stars. Our Sun is one such example. Others include α Cen, Altair, Sirius, Achernar and Barnard's Star. Stars in group B are mostly 6,000 K or cooler yet more luminous than main sequence stars of the same temperature. How can this be? The reason is that these stars are much larger than main sequence stars. Although they emit the same amount of energy per square metre as main sequence stars they have have much greater surface area (area ∝ radius2) the total energy emitted is thus much greater. These stars are referred to as giants. Examples include Aldebaran and Mira. The stars in group C are even more luminous than the giants. These are the supergiants, the largest of stars with extremely high luminosities. A red supergiant such as Betelgeuse would extend beyond the orbit of Jupiter if it replaced the Sun in our solar system.

The final group of interest are those stars in group D. From their position on the H-R diagram we see that they are very hot yet very dim. Although they emit large amounts of energy per square metre they have low luminosity which implies that they must therefore be very small. Group D stars are in fact known as white dwarfs. Sirius B and Procyon B are examples. White dwarfs are much smaller than main sequence stars and are roughly the size of Earth. The diagram below shows the main groups labelled together with example stars in each group. Credit: radius mass But what good does it do? We can make up tables containing hundreds or thousands of stars, with columns for mass, radius, temperature, etc. -- okay. It would help, though, if we could discover just a few simple relationships between these variables; humans are very good at remembering and pondering a few, simple rules, but very bad at remembering thousands and thousands of numbers. Are there any simple relationships hidden in this wealth of data? The answer, of course (why else would I ask the question?) is YES. Let's set the Wayback Machine for the early 1900s, when astronomers first put together the raw numbers for hundreds of stars ....

Hertzsprung and Russell One of the astronomers who gathered together in one place measurements of many stars was the Danish scientist Ejnar Hertzsprung. He wrote several papers in which he identified correlations between different variables. However, since he presented his work in tabular form, it wasn't easy to grasp the signficance of any particular relationship. Moreover, he published in rather obscure journals. As a result, when his work was first published around 1905, it did not make big waves. Several years later, another astronomer dug into the data independently. Henry Norris Russell was a famous scientist at a prestigious institution, Princeton University, so people tended to pay attention to his work. Moreover, he singled out one particular relationship between stellar properties and presented it in a graphical form. In 1913, he described his findings at a meeting of the Royal Astronomical Society. Giant stars and dwarf stars a paper by Russell in which he describes an early version of the HR diagram (the figure to which is lost, alas) His discussion centered on a diagram which showed the absolute magnitude and spectral class of stars.

The very first versions had absolute magntiude on the horizontal axis and spectral class on the vertical axis, but within a year, he switched to the format which has been universally adopted: This figure appears in Russell, Nature, 93, 252 (1914) Long after Russell's graph first appeared, another astronomer pointed out that the same relationship had appeared previously in Hertzsprung's work. We now recognize the achievements of both astronomers by referring to it as the Hertzsprung-Russell diagram, or "HR diagram" for short. What exactly does the diagram show? The vertical axis You may be saying to yourself, "Well, um, okay, so Russell made a diagram. What's the big deal? And what the heck is spectral class, anyway?" Let's go over the diagram slowly. There are several different ways to label the axes, and you may see different combinations in different places. Let's start with the vertical axis: in Russell's original, it shows absolute magnitude. But we can replace this with any measure of the true power output of the star. The two possibilities are absolute magnitude luminosity (usually in solar units) Q: Where are the powerful stars in this diagram?

Q: Where are the feeble stars in this diagram? Right. Powerful at top, feeble at bottom. Q: The Sun has (roughly) absolute magnitude V = 5. Where does it fall in this diagram? How many solar luminosities do stars at the top of the diagram produce? How many solar luminosities do stars at the bottom of the diagram produce? The answers What exactly does the diagram show? The horizontal axis The horizontal axis is, in the original, labelled "spectral class". We will discuss spectral classification soon, but not today. So, we'll replace it with two other quantities which are roughly equivalent, and which frequently appear in its place. You may see any of these three variables on the horizontal axis: spectral class color (or color index) So, for example, if we use color index, the graph would look like this: Q: Where are the hot stars in this diagram? Q: Where are the cool stars in this diagram? Q: Where are the blue stars in this diagram? Q: Where are the red stars in this diagram? Right. Hot, blue stars on the left, cool, red stars on the right. Note that temperature runs backwards on this diagram.

What exactly does the diagram show? Stellar types Now, Russell noticed that the great majority of the stars in the catalogs of his time fell in a band which ran from the upper left to the lower right. He indicated this in his version of the diagram with lines; we now call this region the main sequence. He also noticed the difference in the other two corners of the diagram: there were some stars in the upper right, but very very few stars in the lower left. Hmmmm. What could this mean? Well, think for a moment about these corners. Stars in the upper right region are powerful and cool. Q: How does the temperature of a star affect the power it emits from each square meter of its photosphere? Q: So what does this imply about stars which are both powerful and cool? Right. These stars must be very large -- they must have a very big surface area in order to produce so much power with at such low temperatures. Hertzsprung gave the name giant to the stars with this combination of features, and we have kept it ever since. You often see the term red giant, since most of the stars are reddish.

Now, Hertzsprung and Russell noticed that the red stars came in two varieties: these very powerful, giant stars, in the upper right, and a set of rather feeble stars down in the lower right. If the powerful red stars are called "giants", then the feeble red stars should be called .... "dwarfs." Excerpt from Russell's address to the RAS of June 13, 1913 And so they were (and are). However, Russell realized that these "red dwarfs" were really just the cool end of the main sequence of stars. As a result, he decided to extend the term dwarf to refer to ANY member of the main sequence, not just the red end. So, you may sometimes see these labels on stars: The lower left corner: white dwarfs At the time Hertzsprung and Russell created this diagram, they knew of very few stars which fell in its lower left corner: stars which were hot, yet feeble. Excerpt from Russell's address to the RAS of June 13, 1913 Q: What sort of star could be very hot, yet produce little power? Right.

The only stars which could fall in this region of the HR diagram would be very small stars. And when I write, "very small", I mean "much, much, MUCH smaller than ordinary stars." Just how small would they have to be? Look at Russell's diagram: there is one dot at absolute magnitude (roughly) V = +11 spectral class A, which corresponds to (roughly) T = 10,000 K Q: What is the luminosity of this star? Express your answer in Watts, and in terms of the solar luminosity (3.8 x 1026 Watts). The answer Now, if this star emits radiation like a blackbody, then its luminosity depends simply on its radius R, temperature T, and the Stefan-Boltzmann constant σ = 5.67 x 10-8 Watts per sq.m. per K4. If we know the luminosity and temperature and want to find the radius, we can turn this equation around: Q: Assuming this star emits like a blackbody, figure out its radius in meters. Then compare it to the size of the Sun (which has radius roughly 700,000 km).

The answer Because stars in this region of the diagram are so small, astronomers could not help themselves: they use the term "dwarfs" to refer to these tiny hot stars, even though they do not fall on the main sequence, and even though they are orders of magnitude smaller than the "red dwarfs" at the lower end of the main sequence. Since these stars are hot, though, they receive the name white dwarfs. Summary of the HR diagram The HR diagram is a very useful tool: it shows us at a glance that stars can be placed in just three types "main sequence" or "dwarf" stars, ranging from very hot to very cool, all of (very roughly) the same size "giant" stars, mostly cool, which are tens to hundreds of times larger "white dwarf" stars, which are orders of magnitude smaller than those on the main sequence most stars -- about 90 percent -- fall on the main sequence, with about 10 percent living in the giant area But why should stars break up into these groups? What's the difference between dwarfs and giants? And why are white dwarfs so different from all the other stars? Those are good questions, and kept astronomers occupied for the next several decades ....

For more information Giant stars and dwarf stars a paper by Russell in which he describes an early version of the HR diagram (the figure to which is lost, alas) On the probable order of stellar evolution a paper by Russell, with early thoughts on the connection between the HR diagram and stellar evolution (which turned out to be wrong, but explains some of the jargon we still use) What does the Hertzsprung-Russell diagram show? | Reference.com What does the Hertzsprung-Russell diagram show? A: Quick Answer The Hertzsprung-Russell diagram is a scatter plot that helps illustrate the life cycle of various sizes of stars. It plots four main characteristics: color, absolute magnitude, luminosity and temperature. Full Answer The H-R diagram comes in two types: theoretical, which uses absolute magnitude and temperature; and observational, which uses color and luminosity. Many stars on the H-R diagram fall into the main sequence that all dwarf stars such as the sun follow. They start on the upper-left side of the diagram, which is for hot, bright stars, but gradually cool off. Eventually, dwarf stars expand when all their hydrogen is fused into helium.

Once stars begin fusing helium, lithium, carbon and heavier elements, they create more heat and overcome their gravitational pull, but they eventually lose the ability to generate heat. The H-R diagram classifies stars into five types: white dwarfs, main sequence stars, subgiants, giants and supergiants. All stars eventually leave the main sequence, with the exact process depending on their mass. For example, larger stars explode into a supernova, leaving a dense core that collapses into a neutron star or black hole. Smaller stars go red giant, then collapse into a white dwarf, which gradually burns out. White dwarf stars lack luminosity because of their small size, but they generate a lot of heat from previously being the core of a star that went supernova. Introduction to the Hertzsprung-Russell Diagram AIP Emilio Segre Visual Archives, Margaret Russell Edmondson Collection Henry Norris Russell One of the most useful and powerful plots in astrophysics is the Hertzsprung-Russell diagram (hereafter called the H-R diagram). It originated in 1911 when the Danish astronomer, Ejnar Hertzsprung, plotted the absolute magnitude of stars against their colour (hence effective temperature).

Independently in 1913 the American astronomer Henry Norris Russell used spectral class against absolute magnitude. Their resultant plots showed that the relationship between temperature and luminosity of a star was not random but instead appeared to fall into distinct groups. These are seen in the H-R diagram below. It has a few specific stars included in the plot but otherwise just shows the main regions. The majority of stars, including our Sun, are found along a region called the Main Sequence . Main Sequence stars vary widely in effective temperature but the hotter they are, the more luminous they are, hence the main sequence tends to follow a band going from the bottom right of the diagram to the top left. These stars are fusing hydrogen to helium in their cores. Stars spend the bulk of their existence as main sequence stars. Other major groups of stars found on the H-R diagram are the giants and supergiants; luminous stars that have evolved off the main sequence, and the white dwarfs. Whilst each of these types is discussed in detail in later pages we can use their positions on the H-R diagram to infer some of their properties. Using the H-R Diagram to Infer Stellar Properties Let us look at the cool M-class stars as an example.

If we look at the H-R diagram below we can see that in fact there are three main groups of these stars. At the bottom-right of the diagram we can see two named stars, Proxima Centauri and Barnard's Star. These are both cool (approximately 2,500 K) and dim (absolute magnitudes of about 13, only about 1/10,000 the luminosity of our Sun). Following the broad band straight up we come across Mira, also cool but much more luminous. Travelling further up we come across Antares and Betelgeuse. Again these stars are cool but they are extremely luminous, almost 10,000× as luminous as the Sun. Why do these three groups differ so much in luminosity? The answer to this question depends upon the Stefan-Boltzmann relationship. You may recall from equation 4.4 that the energy emitted per unit surface area per second is simply a function of the fourth power of temperature, that is: l ≈ σT4 (4.4) If two stars have the same effective temperature they each have the same power output per square metre of surface area.

As the H-R diagram however shows that one is much more luminous than the other it must have a greater total power output therefore must have a much greater surface area - the more luminous star is bigger. We can see this from the full expression for luminosity in equation 4.6: L ≈ 4πR2σT4 (4.6) The difference between the three groups of M-class stars is thus a difference in size. This is acknowledged by the names given to each of the groups. The most luminous ones are called supergiants (luminosity classes I and II), the luminous ones are called giants (luminosity class III) and the dim ones are part of the main sequence (luminosity class V) though historically the term dwarf stars was applied to this group. If we look at the vertical band on the H-R diagram for hotter stars around type A spectral class we see a similar pattern: In this case the supergiants Rigel and Deneb have the same effective temperature as Sirius but have extremely high luminosities. They have large radii than Sirius hence greater surface areas and higher luminosities.

Sirius is a main sequence star but because it is hotter than the red main sequence Barnard's Star it is much more luminous than it. If you follow the pink band for hot stars down to the bottom of the H-R diagram you will notice that it intersects another group of stars that includes Procyon B. These are the white dwarfs. They are very hot (about 10,000 K or hotter) therefore emit a lot of energy per second for each square metre of their surface. The fact that they are so dim however, means that they must be extremely small and have a very low surface area. The terminology of white dwarf must not be confused with the old-fashioned term of dwarf stars that was applied to main sequence stars. White dwarfs are very different objects to main sequence stars as we shall see in a later page. Technically they have a luminosity class of wd. Simple calculations provide a size for white dwarfs roughly that of our Earth, less than 1/100 that of the Sun. If we compare the dimmest stars on the H-R diagram we can also make some inferences. The following diagram shows the lower region of the H-R diagram.

Procyon B and Barnard's Star share the same low luminosity with an absolute magnitude of about +13. Procyon B however is much hotter than Barnard's Star thus emits much more energy per second per unit surface area. Given that they have the same total power output Procyon B must therefore have less surface area than Barnard's Star, that is its radius is smaller. Axes on the H-R Diagram This points to an interesting and sometimes confusing feature of the H-R diagram - the scales on the axes. Unlike the height/mass plot earlier in this section, the effective temperature does not increase as it goes from left to right, it actually decreases, that is the highest temperature is on the left-hand side. If colour index (B-V) rather than effective temperature is used then it goes from negative (blue) on the left to positive (red) on the right. A third alternative along the horizontal axis is to use spectral class. Of course, all three quantities are essentially showing the same thing. The diagram below shows the possible axes for an H-R diagram. The vertical axis displays the luminosity of the stars. This is either as a ratio compared with that of the Sun or as absolute magnitude, M.

One point to be careful of when using absolute magnitude is to remember that the lower or more negative the absolute magnitude, the more luminous the star. The brightest stars therefore appear at the top of the H-R diagram with the vertical axis having the most negative value of M at the top. In some circumstances, such as when plotting stars in a specific open or globular cluster, apparent magnitude, m, or V, rather than absolute magnitude may be used. This is valid as all the stars in the cluster are effectively at the same distance away from us hence any differences in apparent magnitude are due to actual difference in luminosity or M. Diagrams where V is plotted against colour index, B-V, are also known as colour-magnitude diagrams. Hertzsprung-Russell Diagram | COSMOS COSMOS - The SAO Encyclopedia of Astronomy › H Hertzsprung-Russell Diagram The Hertzsprung-Russell diagram ( HR diagram ) is one of the most important tools in the study of stellar evolution .

Developed independently in the early 1900s by Ejnar Hertzsprung and Henry Norris Russell, it plots the temperature of stars against their luminosity (the theoretical HR diagram), or the colour of stars (or spectral type ) against their absolute magnitude (the observational HR diagram, also known as a colour-magnitude diagram). Depending on its initial mass , every star goes through specific evolutionary stages dictated by its internal structure and how it produces energy. Each of these stages corresponds to a change in the temperature and luminosity of the star, which can be seen to move to different regions on the HR diagram as it evolves. This reveals the true power of the HR diagram – astronomers can know a star’s internal structure and evolutionary stage simply by determining its position in the diagram. The Hertzsprung-Russell diagram the various stages of stellar evolution. By far the most prominent feature is the main sequence (grey), which runs from the upper left (hot, luminous stars) to the bottom right (cool, faint stars) of the diagram. The giant branch and supergiant stars lie above the main sequence, and white dwarfs are found below it. Credit : R. Hollow, CSIRO.

This Hertzsprung-Russell diagram shows a group of stars in various stages of their evolution. By far the most prominent feature is the main sequence, which runs from the upper left (hot, luminous stars) to the bottom right (cool, faint stars) of the diagram. The giant branch is also well populated and there are many white dwarfs. Also plotted are the Morgan-Keenan luminosity classes that distinguish between stars of the same temperature but different luminosity. --> There are 3 main regions (or evolutionary stages) of the HR diagram: The main sequence stretching from the upper left (hot, luminous stars) to the bottom right (cool, faint stars) dominates the HR diagram. It is here that stars spend about 90% of their lives burning hydrogen into helium in their cores. Main sequence stars have a Morgan-Keenan luminosity class labelled V. red giant and supergiant stars (luminosity classes I through III) occupy the region above the main sequence. They have low surface temperatures and high luminosities which, according to the Stefan-Boltzmann law, means they also have large radii.

Stars enter this evolutionary stage once they have exhausted the hydrogen fuel in their cores and have started to burn helium and other heavier elements. white dwarf stars (luminosity class D) are the final evolutionary stage of low to intermediate mass stars, and are found in the bottom left of the HR diagram. These stars are very hot but have low luminosities due to their small size. The Sun is found on the main sequence with a luminosity of 1 and a temperature of around 5,400 Kelvin . Astronomers generally use the HR diagram to either summarise the evolution of stars, or to investigate the properties of a collection of stars. In particular, by plotting a HR diagram for either a globular or open cluster of stars, astronomers can estimate the age of the cluster from where stars appear to turnoff the main sequence (see the entry on main sequence for how this works). Astronomy Lecture Number 17 H-R Diagram for Stars A Most Important Diagram Classifying stars according to their spectrum is a very powerful way to begin to understand how they work.

As we said last time, the spectral sequence O, B, A, F, G, K, M is a temperature sequence, with the hottest stars being of type O (surface temperatures 30,000-40,000 K), and the coolest stars being of type M (surface temperatures around 3,000 K). Because hot stars are blue, and cool stars are red, the temperature sequence is also a color sequence. It is sometimes helpful, though, to classify objects according to two different properties. Let's say we try to classify stars according to their apparent brightness, also. We could make a plot with color on one axis, and apparent brightness on the other axis, like this: Figure 1: H-R Diagram of apparent brightness versus star color (or temperature). You can see that this classification scheme is not helpful -- the stars are randomly scattered on the plot. Obviously, plotting apparent brightness against color is not helpful, because there are no patterns in the placement of the dots representing stars. They are scattered around randomly. This is because the stars are at all different distances, so the nearby ones appear bright even though they may be intrinsically not so bright.

But what if we look at this same plot, but somehow make sure that the stars are all at the same distance. You know that stars sometimes appear in clusters (because they were all formed out of the same giant cloud, parts of which collapsed to form a lot of stars all around the same time). Here is a photograph of the Pleiades star cluster: Figure 2. If we plot the apparent brightness versus color for such a cluster, where all the stars are the same distance, you get a plot like this: Figure 3. Now you can see that the points representing the stars fall along a clear line in the plot. Such a plot was first made by two astronomers working independently: Ejnar Hertzsprung (Denmark) and Henry Norris Russell (Princeton, USA). This kind of diagram was named after them, as the Hertzsprung-Russell Diagram, or H-R Diagram. It is an extremely powerful diagram for classifying stars and understanding how stars work. We are going to spend the rest of this lecture looking in detail at this diagram. First, though, note the relationship between apparent brightness and absolute brightness that we talked about last time.

We said that astronomers use absolute brightness, which is the apparent brightness stars would have if they were all at the same distance of 10 parsecs. The diagram above uses apparent brightness (apparent magnitudes), but for stars all at the same distance (the distance to the Pleiades star cluster), so it is really a plot of absolute brightness versus color. Or we could plot luminosity versus color, as below: Figure 4. When we know the distances to stars, we can determine their absolute brightness, or luminosity. When we then plot luminosity (or absolute brightness) versus color (or temperature), the stars all fall along a narrow strip in the diagram. This is the H-R Diagram. So the right way to think about an H-R Diagram. It is telling us that a star's color (or temperature) and its luminosity are related. Blue stars are more luminous than red stars. To find this out, though, we have to know the distances to the stars. Remember the star catalog we showed one page of in the last lecture, from the Nearby Stars catalog. We know the distances to these stars, by measuring their parallax. Here is the H-R diagram for that catalog: Figure 5.

Now we see that there is a new region in the lower left, which correspond to faint-blue stars. If blue stars are so luminous, why are these so faint? These are faint because they are very small! They are a class of stars called White Dwarf stars. We can also look at the H-R diagram for other clusters. Here is one for an old cluster of stars, M3, which is a globular cluster: Figure 6 a. Figure 6 b. Now we see a new region of luminous red stars in the upper-right! If red stars are fainter than blue stars, why are these red stars so luminous? It is because they are giant stars, like the star Betelgeuse , which I mentioned last time is so large that, if it were at the distance of the Sun, it would engulf the Earth's orbit, and even the orbit of Mars. These are the Red Giant stars. Patterns in the H-R Diagram We see that the H-R diagram can help us classify different kinds of stars, according to the pattern of where the stars fall in the diagram. The diagonal line that we saw for the Pleiades star cluster represents what we would call normal stars.

The White Dwarfs and Red Giants are different classes of stars that the H-R diagram helps us to identify. So the H-R diagram can tell us something about the size (radius) of the stars. The fact that the H-R diagrams for the nearby stars, the Pleiades star cluster, and the M3 star cluster are all different leads us to look for other differences in these groups of stars that might explain it. It turns out that the difference is the age of the stars. The H-R diagram is going to help us learn something about how stars change as they get older. So you can already see that this is a very powerful diagram indeed. Let's take a look at the overall H-R diagram, including all the different types of stars that we know of. Figure 7. The horizontal axis again shows the color of the stars, and the vertical axis shows the luminosity, in units of the solar luminosity. Note that the tick marks on this vertical, luminosity axis are a factor of 10 apart! A factor of 10 is called an order of magnitude. So the range of luminosity from bottom to top in this diagram is enormous. Each star in the sky can be placed in a unique place on this diagram.

For example, the Sun is a yellow star of 1 solar luminosity (by definition!), so you can find it near the center of the diagram. It falls on the "normal star" line running diagonally from the lower right to the upper left. This is called the Main Sequence. Most stars fall along this line. Radius: Remember that last lecture we said that if we know the temperature and distance to a star we can determine its size. As it turns out, the red stars on the Main Sequence are smaller than the Sun, and the stars get bigger as you go along the Main Sequence toward the hotter (bluer) end. Stars on the Main Sequence that are hotter than the Sun are also larger than the Sun. So hot blue stars are more luminous (and therefore appear higher in this diagram) for two reasons: they are hotter, and hot objects are more luminous than cool objects, but they are also larger. In fact, if a hot star were to get cooler without changing its radius, its luminosity would drop and its color would become more red so that it would follow the diagonal lines in the above diagram. Notice that the White Dwarfs, in the lower left part of the diagram, are parallel with these constant radius lines.

From this we might expect that White Dwarfs get cooler, but stay the same size, as they get older, and we would be right! Other stars also get hotter or cooler during their lifetimes, but they also change size at the same time, so they do not follow these lines. The Red Giant and Red Supergiant parts of the diagram show that these stars are 30 to several hundred times larger in radius than the Sun. We will learn next time that such stars are old, and that the Sun, as it nears the end of its lifetime, will also swell up and become a red giant star. Lifetimes: Notice that there are time markers along the Main Sequence. These are the lifetimes of the stars that are found there. At the spot where the Sun is located, with 1 solar luminosity and a surface temperature of 6,000 K, stars live for about 1010 years, or 10 billion years. Stars that are hotter and more luminous than the Sun live for shorter times, while stars that are cooler and less luminous live for longer times.

This seems reasonable, since more luminous stars must be putting out energy at a higher rate, so they use up their hydrogen "fuel" faster. The hottest stars, of type O and B, live only for 10 million years or less! It is a good thing for us that the Sun is not this kind of star, or else life would never have had time to develop on Earth. Masses: There is a single parameter that accounts for all of the patterns we see on the Main Sequence, and that is the star's mass. If a star develops out of a 10 solar mass cloud, it will become a B star, its surface temperature will be about 20,000 K, it will have a luminosity of about 10,000 Sun's, and it will live for only about 20 million years. All of these characteristics of the star are determined by the initial mass of the cloud, with very little dependence on anything else! So this is the main point to keep in mind. The Main Sequence is a mass sequence.

Higher mass stars will have surface temperatures and luminosities that place at the upper-left end of the Main Sequence, and lower mass stars will have parameters that place them at the lower-right. Numbers of Stars vs. Mass: As it turns out, a giant cloud of gas of hundreds or thousands of solar masses will collapse not to form a single giant star, but will collapse in several places at once (several dense centers) to form many stars. Typically, only a few high-mass stars are formed, and many more of the lower-mass variety are formed. Such a cloud will form a cluster of stars. Because of the lifetime difference, if we look at a young cluster we will see all masses of stars but if we look at an old cluster we will see only the smaller mass stars. Why? Because the high-mass stars have already lived their lives out and died (we will discuss how stars die later). Compare the young Pleiades cluster (figures 2 and 3, above), with the much older M3 cluster (figure 6 a and b). The Pleiades has a few very bright stars and lots of less luminous (lower-mass) stars.

The M3 cluster has only fainter stars on the main sequence. It also has lots of Red Giants, but that is another story. If we look at the stars in our neighborhood (figure 5), we see far more low-mass stars. So most stars in the galaxy today are low-mass stars, for two reasons: 1) more low-mass than high-mass stars are born in each cloud, and 2) low-mass stars live much much longer than high-mass stars. Main Sequence Turn-off: If you look at the M3 cluster H-R diagram (figure 6b), you see that the main sequence only extends part way to the upper-left, and then the stars appear off the main sequence to the upper right, in the Red Giant area of the H-R diagram. This is because when stars age, they get cooler (which makes them turn red) and larger (which makes them more luminous), so they actually become Red Giants. If we look at an H-R diagram for several clusters of different ages, here is what we see: Figure 8 Really young clusters like the Double Cluster h and chi Persei have high-mass O stars at the upper end of the Main Sequence.

Older clusters like the Pleiades have B stars starting to age off the Main Sequence. The Hyades, even holder, is starting to have A stars leave the Main Sequence, and the much older NGC 188 has F stars leaving the Main Sequence. This aging off the Main Sequence is called the Main Sequence Turn-off, and we can use it to actually tell how old clusters are. The oldest clusters in our galaxy are about 14 billion years old, which is one way we know how old the Universe is. The Hertzsprung-Russell (HR) diagram Copyright © Michael Richmond. This work is licensed under a Creative Commons License . The Hertzsprung-Russell (HR) diagram If you look carefully at stars in the sky, you'll see that they aren't all the same color. Some are reddish, some yellowish, some blueish. The effect is subtle, but you can see it if you try. Taken from APOD. Credit and Copyright: Stefan Seip Is there some way we can use these colors to determine properties of the stars? The Hipparcos satellite measured the distances to hundreds of thousands of stars.

It also measured the magnitude of each star through two filters: A blue filter, yielding a B (for "blue") magnitude A greenish filter, yielding a V (for "visual") magnitude (the human eye has highest sensitivity in the green) Now, astronomers call the difference between the B and V magnitude of a star its (B-V) color, or sometimes just "color" for short. Remember how magnitudes work: large numbers mean "faint", and small numbers mean "bright". What is the "(B-V) color" of a hot star? Hot stars emit most of their light at short wavelengths: in the blue and ultraviolet. So when we measure their light through filters, we see B filter: lots of light, therefore small magnitude V filter: less light, therefore larger magnitude And the result is that (B-V) is (small - large) = negative. So very hot stars have negative (B-V) colors. On the other hand, cool stars emit most of their light in the red part of the spectrum.

So when we measure their light through filters, we see B filter: little light, therefore large magnitude V filter: more light, therefore smaller magnitude And the result is that (B-V) is (large - small) = positive. So cool stars have positive (B-V) colors. In short, (B-V) color temperature ---------------- ------------ small (< 0.5) hot big (> 2.0) cool To recap, Hipparcos measured three quantities for each star: distance apparent B magnitude, or apparent brightness in blue light apparent V magnitude, or apparent brightness in green light We can use the inverse square law to turn the distance and apparent brightness into absolute B magnitude, which is similar to luminosity in blue light absolute V magnitude, which is similar to luminosity in green light "Absolute magnitude" is defined as the magnitude a star would have if we picked it up and placed it exactly 10 parsecs away from the Sun; that's very roughly as close as the star Vega, and a bit more distant than the Sun's closest neighbors.

Astronomers long ago worked through all the math to come up with a formula which converts apparent magnitude and distance into absolute magnitude: (abs mag M) = (app mag m) + 5 - 5 * (log d) where absolute magnitude is the capital M apparent magnitude is the lower-case m d is the distance to the star in parsecs "log" is the logarithm base 10 function Let's practice converting apparent magnitudes to absolute magnitudes. Q: The star Deneb, in Cygnus the Swan, has an apparent magnitude m = 1.26 and a distance d = 500 parsecs. What is its absolute magnitude? Q: The Sun has an apparent magnitude m = -26.5. What is its absolute magnitude? (You must convert its distance into parsecs -- see Appendix A). What can we do with this information? Hmmm. Is there any relationship which might suggest a fundamental physical property of the stars? Well, we can try plotting various quantities against each other, and looking for something "meaningful." Let's try plotting color on the horizontal axis, and apparent V magnitude on the vertical axis. Hmmm.

That looks almost like random scatter, although it does show that there are lots of stars with (B-V) colors around 0.5 (which corresponds to temperatures around 6000 or 7000 Kelvin). But wait -- since we know the distance to each star, we can convert its apparent magnitude (how bright it appears in our sky) to its absolute magnitude (how much power it actually radiates). Let's try plotting absolute V magnitude against color. Aha! When we look at the stars in this way, most of them (over 90%) fall along a diagonal strip running from upper left to lower right. This curious fact was first noticed back in the early 1900s by two astronomers, American Henry Norris Russell and Dane Ejnar Hertzsprung. As a result, this sort of graph is called a Hertzsprung-Russell diagram, or "HR diagram" for short. Norris and Russell called the diagonal strip along which most stars fall the main sequence. What does this mean?

It makes more sense if we convert the units into some equivalents: we can turn (B-V) color into temperature: red means cool, blue means hot absolute V magnitude into luminosity: small means powerful, large means feeble. We can express luminosity in solar units: how many times more powerful is the star than the Sun? If plot these quantities, the HR diagram looks like this: No, your eyes aren't failing. There are sharp edges in the diagram above, due to the approximation I used to convert color into temperature. Once again you may ask: what does this mean? What it means is that most stars are roughly the same size. Remember that hot objects radiate more light than cool ones. If two objects are the same size, then their luminosities are simply 4 Luminosity (A) [ Temperature (A) ] ----------------- = [ ------------------ ] Luminosity (B) [ Temperature (B) ] Use this rule to figure out: Q: Where would a star of the Sun's size, but T = 15,000 K, fall on the HR diagram?

Q: Where would a star of the Sun's size, but T = 2,800 K, fall on the HR diagram? You can see that the main sequence can be explained mostly due to differences in temperature: hot stars fall on the upper left, cool stars on the lower right portion of the sequence. But that doesn't tell the whole story: stars hotter than the Sun are apparently a bit larger than the Sun, and cooler stars are a bit smaller. These differences in size are only factors of two or three. Hmmm. This tells us one thing -- most stars are roughly the same size as the Sun -- but leaves us asking two more questions: Why are most stars roughly the same size as the Sun? Why are a bunch of stars (the ones in the upper right-hand corner of the HR diagram) apparently much larger? For more information H-R Diagram Hertzsprung-Russell Diagram The Hertzsprung-Russell Diagram is a graphical tool that astronomers use to classify stars according to their luminosity, spectral type, color, temperature and evolutionary stage. Stars in the stable phase of hydrogen burning lie along the Main Sequence according to their mass.

After a star uses up all the hydrogen in its core, it leaves the main sequence and moves towards the red giant branch. The most massive stars may also become red supergiants, in the upper right corner of the diagram. The lower left corner is reserved for the white dwarfs.

Question: What appear on a Hertzsprung-Russell diagram?
Answer: Stars